Protein-mediated DNA looping, which occurs when a linker protein binds to two operator sites on the same DNA molecule, is an important regulatory element of many biological processes such as transcription and DNA replication. In physiologic conditions, the conformation of DNA undergoes thermal fluctuations which enable the operators to align for looping. The likelihood for the operator sites to align can be significantly altered by mechanically constraining the substrate DNA. For instance, tension extends DNA and increases the free energy of operator alignment. By modeling DNA as a wormlike chain, we use statistical mechanics to show that when the loop size is greater than 100bp a tension of 500 femtonewtons can increase the time required for loop closure by two orders of magnitude. This force is small compared to the piconewton forces that are associated with RNA polymerases and other molecular motors, indicating that intracellular mechanical forces might affect transcriptional regulation. We propose that supercoiling of DNA may help to stabilize the looping process against the disruptive effective of tension. Since DNA looping is important in gene regulation and genetic transformation, our theory suggests that thermal fluctuations and response to mechanical constraints play an important role in a living cell. Indeed, recent micromechanical measurements on DNA looping have verified the importance of mechanical constraints. Besides providing perspective on these experiments we offer suggestions for future micromechanical studies.